If the homography matrix of Image 1 to Image 2 is given, and another homography matrix for image 2 to image 3 is given, how do I calculate the homography matrix for image 1 to image 3?
PS : I need the homorgraphy matrices to be 3x3 only because I would be working on a large dataset.
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Consider three points $A$ in image 1,$B$ in image 2 and $C$ in image 3.$H1$ is the homography matrix from $A$ to $B$ and $H2$ is the homography matrix from $B$ to $C$. Then,
$$B = H1A$$
$$C = H2B$$
Substituting for B from first equation
$$C = H2(H1A)$$
Due to matrix associative property,
$$C = (H2H1)A$$
The homography matrix from $A$ to $C$ is given by $H2H1$.
